How do you find the probability of an event given the odds of the event occurring is 2:1?

1 Answer
Mar 16, 2018

The desired probability is $\frac{2}{3}$

Explanation:

Probabilities always range between $0$ and $1$.

The odds on the other hand are defined as the probability that the event will occur divided by the probability that the event will not occur.

As odds of the event occurring is $2 : 1$

the probability that the event will occur is twice the probability that the event will not occur.

But if probabilty of happening of event is $p$, probability of event not happening is $1 - p$

Hence $\frac{p}{1 - p} = 2$ or $p = 2 - 2 p$ or $3 p = 2$ i.e. $p = \frac{2}{3}$

and desired probability is $\frac{2}{3}$.